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Magnet Lattice

coupled dipoles on a grid

Draw

Click an empty cell to add a magnet, click a magnet to remove it. Drag a magnet to set its angle (hold Shift to snap to 15°).

Right/middle-drag to pan, mouse-wheel to zoom, 0 resets the view.

Magnets0

Grid

Stable states

Relaxes from structured seeds and many random starts, keeps every stationary point and merges states related by a lattice rotation/reflection or a global flip. Click an entry to load it; sweeping again extends the catalog.

Random starts

Transitions

For every stable state, bisects the smallest perturbation — per core (±), per normal mode (±) and along random directions — that escapes its basin, and where it lands. Escapes into uncatalogued minima seed a follow-up sweep. Extra probes spot-check that each ray is monotone (⚠ otherwise). Nodes sit by energy; edge width ∝ count, label = energy climbed along the ray.

Random directions per state

Normal modes

Show coupling lines (red H_ij>0, blue <0)

Dragging a magnet here changes the configuration and invalidates computed modes.

Coupling matrix

Eigen-spectrum

Click a bar (or press ←/→) to select a mode. Hover the coupling matrix to highlight the pair.

Mode 0

ω = 0